R. Hakl, A. Lomtatidze, and B. Puza

On nonnegative solutions of first order scalar functional differential equations

abstract:
Nonimprovable effective sufficient conditions are established for the existence and uniqueness of a nonnegative solution of the problem $$ u'(t)=\ell(u)(t)+q(t),\qquad u(a)=c\qquad (u(b)=c), $$ where $\ell:C([a,b];R)\to L([a,b];R)$ is a linear bounded operator, $q\in L([a,b];R_+)$ ($q\in L([a,b];R_-)$) and $c\in R_+$.

Mathematics Subject Classification: 34K06, 34K12.

Key words and phrases: Linear functional differential equations, nonnegative solution, theorem on functional differential inequalities.